ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary We consider a vector-valued function u ε W loc 1, q (Ω;R N),Ω ⊂R N,which is a weak solution of the elliptic system: $$\begin{array}{*{20}c} { - \sum\limits_{i = 1}^n {D_i \{ a_\alpha ^i (x,Du(x))\} = 0,} } & {\alpha = 1,...,N.} \\ \end{array}$$ If the so- called «p, q- growth conditions» hold, then we prove that: $$\begin{array}{*{20}c} {(1 + |Du|^2 )^{{P \mathord{\left/ {\vphantom {P 4}} \right. \kern-\nulldelimiterspace} 4}} \in W_{loc}^{1,2} (\Omega );} & {x \to a_\alpha ^i (x,Du(x)) \in W_{loc}^{1,{q \mathord{\left/ {\vphantom {q {(q - 1)}}} \right. \kern-\nulldelimiterspace} {(q - 1)}}} (\Omega );} & {u \in } \\ \end{array} W_{loc}^{2,2} (\Omega ;R^N ).$$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01760015
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